Student Probability Seminar

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Oriented Planar Maps and Annular Imaginary Geometry

Speaker: Zhenfeng Tu, CIMS

Location: Warren Weaver Hall 1314

Date: Monday, March 10, 2025, 11 a.m.

Synopsis:

We consider a class of random orientations on annular maps, which is in bijection with lattice random walks that, in the scaling limit, converges to a correlated Brownian path measure. We then showed a Mating-of-Trees type result, by showing that the correlated Brownian path measure is the boundary length process of a curve decorated annulus. We also computed the law of the modulus of the annulus. This extends (Kenyon, Miller, Sheffield and Wilson, 2019) and answers a question therewithin. This is based on joint work with Xingjian Di and Nina Holden.